1. 2. 3. 4. 5. 6. Determine whether each function is convex, concave or neither. f(x)...
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1. 2. 3. 4. 5. 6. Determine whether each function is convex, concave or neither. f(x) = e²x + x4 f(x, y) = x³ + 3xy + y² a. b. Find the values of a, b, and c such that f(x, y) = ax² + bxy + cy² is a concave function Use the following function to construct a convex set z = x² + ey By drawing sketches, decide if the sets {(x, y) = R² y ≤ x²} are convex or not A company produces two goods sold in two separate markets, where P₁ = 200-40₁ - 3Qz P₂ = 230-501 - 202 TC = 2Q1 +2Q1 Q₂ + 4Q²/² Total profit: = (P₁Q₁ + P₂Q₂) - TC Find values of Q1 and Q2 where total profit is maximized and check the second order condition One firm producing 3 goods under perfect competition: TR = P1Q1 + P₂Q2 + P3Q3 TC = Q² + Q² + Q3 Find profit maximizing quantity of good 1 and good 2, good 3. Check that they satisfy the maximum condition. a. b. 1. 2. 3. 4. 5. 6. Determine whether each function is convex, concave or neither. f(x) = e²x + x4 f(x, y) = x³ + 3xy + y² a. b. Find the values of a, b, and c such that f(x, y) = ax² + bxy + cy² is a concave function Use the following function to construct a convex set z = x² + ey By drawing sketches, decide if the sets {(x, y) = R² y ≤ x²} are convex or not A company produces two goods sold in two separate markets, where P₁ = 200-40₁ - 3Qz P₂ = 230-501 - 202 TC = 2Q1 +2Q1 Q₂ + 4Q²/² Total profit: = (P₁Q₁ + P₂Q₂) - TC Find values of Q1 and Q2 where total profit is maximized and check the second order condition One firm producing 3 goods under perfect competition: TR = P1Q1 + P₂Q2 + P3Q3 TC = Q² + Q² + Q3 Find profit maximizing quantity of good 1 and good 2, good 3. Check that they satisfy the maximum condition. a. b.
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1 Determine whether each function is convex concave or neither a To determine the convexity of fx e2x x we need to check the second derivative fx ddxe2x x ddx2e2x 1 4e2x Since fx 4e2x is positive for ... View the full answer
Related Book For
Applied Regression Analysis and Other Multivariable Methods
ISBN: 978-1285051086
5th edition
Authors: David G. Kleinbaum, Lawrence L. Kupper, Azhar Nizam, Eli S. Rosenberg
Posted Date:
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